Question

Consider the following equations. y = x, y = x5 Sketch the region bounded by the graphs of the equations. y Find the area of the region. 1 2 -2 -2 -1 y 2 1 -2

Answer 1

The total area of the regions between the curves is 1/3 square units

Calculating the total area of the regions between the curves

From the question, we have the following parameters that can be used in our computation:

y = x and y = x⁵

With the use of graphs, the curves intersect at

x = 0 and x = 1

So, the area of the regions between the curves is

Area = ∫x⁵ - x dx

Integrate

Area = x⁶/6 - x²/2

Recall that x = 0 and x = 1

So, we have

Area = -1⁶/6 + 1²/2

Evaluate

Area = 1/3

Hence, the total area of the regions between the curves is 1/3 square units